"I actually am....." sounds a little strange. I would avoid it. As for the others, they seem to work pretty much the same.
So, you're not going to the game?
Actually, I am. I changed my mind. (Used for emphasis.)
I am, actually. I changed my mind. (Again for emphasis.)
Note that you need a comma in this type of sentence.
Actually means 'in fact' (de fato) when used this way. Sometimes we use it as an intensifier in the same way as 'really'
I actually thought that she liked me. How wrong can you be?
I really thought that she liked me. How wrong can you be?
As an intensifier it goes before the verb.